Answer
$240\;\rm nm$
Work Step by Step
As we see in the figure below, the two reflected rays experience a $\pi$ phase change due to reflection from a medium with a greater index of refraction.
For constructive interference from the film when the two rays are reflected in phase, the path length difference is given by
$$2t=m\lambda_n=\dfrac{m\lambda}{n_{coating}}$$
And hence the thickness of the film is given by
$$t=\dfrac{m\lambda}{2n_{coating}}$$
At $m=0$, the thickness will be zero which means there is no coating at all.
So, we can work with $m=1$ for the minimum thickness needed.
$$t=\dfrac{ \lambda}{2n_{coating}}$$
For red light;
$$t=\dfrac{ 643}{2\cdot 1.34}=\color{red}{\bf 240}\;\rm nm$$